%------------------------------------------------------------------------------ % File : ePrincess---1.0 % Problem : SET143+4 : TPTP v8.1.0. Released v2.2.0. % Transfm : none % Format : tptp:raw % Command : ePrincess-casc -timeout=%d %s % Computer : n017.cluster.edu % Model : x86_64 x86_64 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz % Memory : 8042.1875MB % OS : Linux 3.10.0-693.el7.x86_64 % CPULimit : 300s % WCLimit : 600s % DateTime : Tue Jul 19 00:17:53 EDT 2022 % Result : Theorem 3.95s 1.66s % Output : Proof 6.30s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.04/0.14 % Problem : SET143+4 : TPTP v8.1.0. Released v2.2.0. % 0.04/0.14 % Command : ePrincess-casc -timeout=%d %s % 0.14/0.36 % Computer : n017.cluster.edu % 0.14/0.36 % Model : x86_64 x86_64 % 0.14/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.14/0.36 % Memory : 8042.1875MB % 0.14/0.36 % OS : Linux 3.10.0-693.el7.x86_64 % 0.14/0.36 % CPULimit : 300 % 0.14/0.36 % WCLimit : 600 % 0.14/0.36 % DateTime : Sat Jul 9 21:13:17 EDT 2022 % 0.14/0.36 % CPUTime : % 0.61/0.67 ____ _ % 0.61/0.67 ___ / __ \_____(_)___ ________ __________ % 0.61/0.67 / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/ % 0.61/0.67 / __/ ____/ / / / / / / /__/ __(__ |__ ) % 0.61/0.67 \___/_/ /_/ /_/_/ /_/\___/\___/____/____/ % 0.61/0.67 % 0.61/0.67 A Theorem Prover for First-Order Logic % 0.61/0.67 (ePrincess v.1.0) % 0.61/0.67 % 0.61/0.67 (c) Philipp Rümmer, 2009-2015 % 0.61/0.67 (c) Peter Backeman, 2014-2015 % 0.61/0.67 (contributions by Angelo Brillout, Peter Baumgartner) % 0.61/0.67 Free software under GNU Lesser General Public License (LGPL). % 0.61/0.67 Bug reports to peter@backeman.se % 0.61/0.67 % 0.61/0.67 For more information, visit http://user.uu.se/~petba168/breu/ % 0.61/0.67 % 0.61/0.67 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ... % 0.73/0.72 Prover 0: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all % 1.62/1.00 Prover 0: Preprocessing ... % 2.08/1.19 Prover 0: Warning: ignoring some quantifiers % 2.08/1.22 Prover 0: Constructing countermodel ... % 2.75/1.38 Prover 0: gave up % 2.75/1.39 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -resolutionMethod=normal +ignoreQuantifiers -generateTriggers=all % 2.75/1.41 Prover 1: Preprocessing ... % 3.18/1.51 Prover 1: Constructing countermodel ... % 3.95/1.66 Prover 1: proved (277ms) % 3.95/1.66 % 3.95/1.66 No countermodel exists, formula is valid % 3.95/1.66 % SZS status Theorem for theBenchmark % 3.95/1.66 % 3.95/1.66 Generating proof ... found it (size 81) % 5.87/2.08 % 5.87/2.08 % SZS output start Proof for theBenchmark % 5.87/2.08 Assumed formulas after preprocessing and simplification: % 5.87/2.08 | (0) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : ( ~ (v7 = 0) & intersection(v3, v2) = v4 & intersection(v1, v2) = v5 & intersection(v0, v5) = v6 & intersection(v0, v1) = v3 & equal_set(v4, v6) = v7 & ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : (v12 = 0 | ~ (product(v9) = v10) | ~ (member(v8, v11) = v12) | ~ (member(v8, v10) = 0) | ? [v13] : ( ~ (v13 = 0) & member(v11, v9) = v13)) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : (v12 = 0 | ~ (difference(v10, v9) = v11) | ~ (member(v8, v11) = v12) | ? [v13] : ? [v14] : (member(v8, v10) = v13 & member(v8, v9) = v14 & ( ~ (v13 = 0) | v14 = 0))) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : (v12 = 0 | ~ (union(v9, v10) = v11) | ~ (member(v8, v11) = v12) | ? [v13] : ? [v14] : ( ~ (v14 = 0) & ~ (v13 = 0) & member(v8, v10) = v14 & member(v8, v9) = v13)) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : (v12 = 0 | ~ (intersection(v9, v10) = v11) | ~ (member(v8, v11) = v12) | ? [v13] : ? [v14] : (member(v8, v10) = v14 & member(v8, v9) = v13 & ( ~ (v14 = 0) | ~ (v13 = 0)))) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : (v11 = 0 | ~ (sum(v9) = v10) | ~ (member(v8, v12) = 0) | ~ (member(v8, v10) = v11) | ? [v13] : ( ~ (v13 = 0) & member(v12, v9) = v13)) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v11 = 0 | ~ (product(v9) = v10) | ~ (member(v8, v10) = v11) | ? [v12] : ? [v13] : ( ~ (v13 = 0) & member(v12, v9) = 0 & member(v8, v12) = v13)) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v11 = 0 | ~ (unordered_pair(v9, v8) = v10) | ~ (member(v8, v10) = v11)) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v11 = 0 | ~ (unordered_pair(v8, v9) = v10) | ~ (member(v8, v10) = v11)) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v11 = 0 | ~ (power_set(v9) = v10) | ~ (member(v8, v10) = v11) | ? [v12] : ( ~ (v12 = 0) & subset(v8, v9) = v12)) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v10 = v8 | v9 = v8 | ~ (unordered_pair(v9, v10) = v11) | ~ (member(v8, v11) = 0)) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v9 = v8 | ~ (unordered_pair(v11, v10) = v9) | ~ (unordered_pair(v11, v10) = v8)) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v9 = v8 | ~ (difference(v11, v10) = v9) | ~ (difference(v11, v10) = v8)) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v9 = v8 | ~ (union(v11, v10) = v9) | ~ (union(v11, v10) = v8)) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v9 = v8 | ~ (intersection(v11, v10) = v9) | ~ (intersection(v11, v10) = v8)) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v9 = v8 | ~ (equal_set(v11, v10) = v9) | ~ (equal_set(v11, v10) = v8)) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v9 = v8 | ~ (subset(v11, v10) = v9) | ~ (subset(v11, v10) = v8)) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v9 = v8 | ~ (member(v11, v10) = v9) | ~ (member(v11, v10) = v8)) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : ( ~ (difference(v10, v9) = v11) | ~ (member(v8, v11) = 0) | ? [v12] : ( ~ (v12 = 0) & member(v8, v10) = 0 & member(v8, v9) = v12)) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : ( ~ (union(v9, v10) = v11) | ~ (member(v8, v11) = 0) | ? [v12] : ? [v13] : (member(v8, v10) = v13 & member(v8, v9) = v12 & (v13 = 0 | v12 = 0))) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : ( ~ (intersection(v9, v10) = v11) | ~ (member(v8, v11) = 0) | (member(v8, v10) = 0 & member(v8, v9) = 0)) & ! [v8] : ! [v9] : ! [v10] : (v10 = 0 | ~ (singleton(v8) = v9) | ~ (member(v8, v9) = v10)) & ! [v8] : ! [v9] : ! [v10] : (v10 = 0 | ~ (equal_set(v8, v9) = v10) | ? [v11] : ? [v12] : (subset(v9, v8) = v12 & subset(v8, v9) = v11 & ( ~ (v12 = 0) | ~ (v11 = 0)))) & ! [v8] : ! [v9] : ! [v10] : (v10 = 0 | ~ (subset(v8, v9) = v10) | ? [v11] : ? [v12] : ( ~ (v12 = 0) & member(v11, v9) = v12 & member(v11, v8) = 0)) & ! [v8] : ! [v9] : ! [v10] : (v9 = v8 | ~ (product(v10) = v9) | ~ (product(v10) = v8)) & ! [v8] : ! [v9] : ! [v10] : (v9 = v8 | ~ (sum(v10) = v9) | ~ (sum(v10) = v8)) & ! [v8] : ! [v9] : ! [v10] : (v9 = v8 | ~ (singleton(v10) = v9) | ~ (singleton(v10) = v8)) & ! [v8] : ! [v9] : ! [v10] : (v9 = v8 | ~ (singleton(v9) = v10) | ~ (member(v8, v10) = 0)) & ! [v8] : ! [v9] : ! [v10] : (v9 = v8 | ~ (power_set(v10) = v9) | ~ (power_set(v10) = v8)) & ! [v8] : ! [v9] : ! [v10] : ( ~ (sum(v9) = v10) | ~ (member(v8, v10) = 0) | ? [v11] : (member(v11, v9) = 0 & member(v8, v11) = 0)) & ! [v8] : ! [v9] : ! [v10] : ( ~ (power_set(v9) = v10) | ~ (member(v8, v10) = 0) | subset(v8, v9) = 0) & ! [v8] : ! [v9] : ! [v10] : ( ~ (subset(v8, v9) = 0) | ~ (member(v10, v8) = 0) | member(v10, v9) = 0) & ! [v8] : ! [v9] : ( ~ (equal_set(v8, v9) = 0) | (subset(v9, v8) = 0 & subset(v8, v9) = 0)) & ! [v8] : ~ (member(v8, empty_set) = 0)) % 6.09/2.12 | Instantiating (0) with all_0_0_0, all_0_1_1, all_0_2_2, all_0_3_3, all_0_4_4, all_0_5_5, all_0_6_6, all_0_7_7 yields: % 6.09/2.12 | (1) ~ (all_0_0_0 = 0) & intersection(all_0_4_4, all_0_5_5) = all_0_3_3 & intersection(all_0_6_6, all_0_5_5) = all_0_2_2 & intersection(all_0_7_7, all_0_2_2) = all_0_1_1 & intersection(all_0_7_7, all_0_6_6) = all_0_4_4 & equal_set(all_0_3_3, all_0_1_1) = all_0_0_0 & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | ~ (product(v1) = v2) | ~ (member(v0, v3) = v4) | ~ (member(v0, v2) = 0) | ? [v5] : ( ~ (v5 = 0) & member(v3, v1) = v5)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | ~ (difference(v2, v1) = v3) | ~ (member(v0, v3) = v4) | ? [v5] : ? [v6] : (member(v0, v2) = v5 & member(v0, v1) = v6 & ( ~ (v5 = 0) | v6 = 0))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | ~ (union(v1, v2) = v3) | ~ (member(v0, v3) = v4) | ? [v5] : ? [v6] : ( ~ (v6 = 0) & ~ (v5 = 0) & member(v0, v2) = v6 & member(v0, v1) = v5)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | ~ (intersection(v1, v2) = v3) | ~ (member(v0, v3) = v4) | ? [v5] : ? [v6] : (member(v0, v2) = v6 & member(v0, v1) = v5 & ( ~ (v6 = 0) | ~ (v5 = 0)))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v3 = 0 | ~ (sum(v1) = v2) | ~ (member(v0, v4) = 0) | ~ (member(v0, v2) = v3) | ? [v5] : ( ~ (v5 = 0) & member(v4, v1) = v5)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (product(v1) = v2) | ~ (member(v0, v2) = v3) | ? [v4] : ? [v5] : ( ~ (v5 = 0) & member(v4, v1) = 0 & member(v0, v4) = v5)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (unordered_pair(v1, v0) = v2) | ~ (member(v0, v2) = v3)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (unordered_pair(v0, v1) = v2) | ~ (member(v0, v2) = v3)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (power_set(v1) = v2) | ~ (member(v0, v2) = v3) | ? [v4] : ( ~ (v4 = 0) & subset(v0, v1) = v4)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v2 = v0 | v1 = v0 | ~ (unordered_pair(v1, v2) = v3) | ~ (member(v0, v3) = 0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (unordered_pair(v3, v2) = v1) | ~ (unordered_pair(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (difference(v3, v2) = v1) | ~ (difference(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (union(v3, v2) = v1) | ~ (union(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (intersection(v3, v2) = v1) | ~ (intersection(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (equal_set(v3, v2) = v1) | ~ (equal_set(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (subset(v3, v2) = v1) | ~ (subset(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (member(v3, v2) = v1) | ~ (member(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (difference(v2, v1) = v3) | ~ (member(v0, v3) = 0) | ? [v4] : ( ~ (v4 = 0) & member(v0, v2) = 0 & member(v0, v1) = v4)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (union(v1, v2) = v3) | ~ (member(v0, v3) = 0) | ? [v4] : ? [v5] : (member(v0, v2) = v5 & member(v0, v1) = v4 & (v5 = 0 | v4 = 0))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (intersection(v1, v2) = v3) | ~ (member(v0, v3) = 0) | (member(v0, v2) = 0 & member(v0, v1) = 0)) & ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (singleton(v0) = v1) | ~ (member(v0, v1) = v2)) & ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (equal_set(v0, v1) = v2) | ? [v3] : ? [v4] : (subset(v1, v0) = v4 & subset(v0, v1) = v3 & ( ~ (v4 = 0) | ~ (v3 = 0)))) & ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (subset(v0, v1) = v2) | ? [v3] : ? [v4] : ( ~ (v4 = 0) & member(v3, v1) = v4 & member(v3, v0) = 0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (product(v2) = v1) | ~ (product(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (sum(v2) = v1) | ~ (sum(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (singleton(v2) = v1) | ~ (singleton(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (singleton(v1) = v2) | ~ (member(v0, v2) = 0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (power_set(v2) = v1) | ~ (power_set(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (sum(v1) = v2) | ~ (member(v0, v2) = 0) | ? [v3] : (member(v3, v1) = 0 & member(v0, v3) = 0)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (power_set(v1) = v2) | ~ (member(v0, v2) = 0) | subset(v0, v1) = 0) & ! [v0] : ! [v1] : ! [v2] : ( ~ (subset(v0, v1) = 0) | ~ (member(v2, v0) = 0) | member(v2, v1) = 0) & ! [v0] : ! [v1] : ( ~ (equal_set(v0, v1) = 0) | (subset(v1, v0) = 0 & subset(v0, v1) = 0)) & ! [v0] : ~ (member(v0, empty_set) = 0) % 6.09/2.13 | % 6.09/2.13 | Applying alpha-rule on (1) yields: % 6.09/2.13 | (2) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (subset(v3, v2) = v1) | ~ (subset(v3, v2) = v0)) % 6.09/2.13 | (3) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (member(v3, v2) = v1) | ~ (member(v3, v2) = v0)) % 6.09/2.13 | (4) ! [v0] : ! [v1] : ! [v2] : ( ~ (subset(v0, v1) = 0) | ~ (member(v2, v0) = 0) | member(v2, v1) = 0) % 6.09/2.13 | (5) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (union(v1, v2) = v3) | ~ (member(v0, v3) = 0) | ? [v4] : ? [v5] : (member(v0, v2) = v5 & member(v0, v1) = v4 & (v5 = 0 | v4 = 0))) % 6.09/2.13 | (6) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (unordered_pair(v1, v0) = v2) | ~ (member(v0, v2) = v3)) % 6.09/2.13 | (7) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (equal_set(v3, v2) = v1) | ~ (equal_set(v3, v2) = v0)) % 6.09/2.13 | (8) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (product(v1) = v2) | ~ (member(v0, v2) = v3) | ? [v4] : ? [v5] : ( ~ (v5 = 0) & member(v4, v1) = 0 & member(v0, v4) = v5)) % 6.09/2.13 | (9) ! [v0] : ~ (member(v0, empty_set) = 0) % 6.09/2.13 | (10) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v3 = 0 | ~ (sum(v1) = v2) | ~ (member(v0, v4) = 0) | ~ (member(v0, v2) = v3) | ? [v5] : ( ~ (v5 = 0) & member(v4, v1) = v5)) % 6.09/2.13 | (11) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (union(v3, v2) = v1) | ~ (union(v3, v2) = v0)) % 6.09/2.13 | (12) ~ (all_0_0_0 = 0) % 6.09/2.13 | (13) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | ~ (intersection(v1, v2) = v3) | ~ (member(v0, v3) = v4) | ? [v5] : ? [v6] : (member(v0, v2) = v6 & member(v0, v1) = v5 & ( ~ (v6 = 0) | ~ (v5 = 0)))) % 6.09/2.14 | (14) ! [v0] : ! [v1] : ! [v2] : ( ~ (sum(v1) = v2) | ~ (member(v0, v2) = 0) | ? [v3] : (member(v3, v1) = 0 & member(v0, v3) = 0)) % 6.09/2.14 | (15) intersection(all_0_6_6, all_0_5_5) = all_0_2_2 % 6.09/2.14 | (16) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | ~ (union(v1, v2) = v3) | ~ (member(v0, v3) = v4) | ? [v5] : ? [v6] : ( ~ (v6 = 0) & ~ (v5 = 0) & member(v0, v2) = v6 & member(v0, v1) = v5)) % 6.09/2.14 | (17) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (unordered_pair(v0, v1) = v2) | ~ (member(v0, v2) = v3)) % 6.09/2.14 | (18) intersection(all_0_7_7, all_0_2_2) = all_0_1_1 % 6.09/2.14 | (19) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | ~ (product(v1) = v2) | ~ (member(v0, v3) = v4) | ~ (member(v0, v2) = 0) | ? [v5] : ( ~ (v5 = 0) & member(v3, v1) = v5)) % 6.09/2.14 | (20) intersection(all_0_7_7, all_0_6_6) = all_0_4_4 % 6.09/2.14 | (21) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v2 = v0 | v1 = v0 | ~ (unordered_pair(v1, v2) = v3) | ~ (member(v0, v3) = 0)) % 6.09/2.14 | (22) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (equal_set(v0, v1) = v2) | ? [v3] : ? [v4] : (subset(v1, v0) = v4 & subset(v0, v1) = v3 & ( ~ (v4 = 0) | ~ (v3 = 0)))) % 6.09/2.14 | (23) ! [v0] : ! [v1] : ( ~ (equal_set(v0, v1) = 0) | (subset(v1, v0) = 0 & subset(v0, v1) = 0)) % 6.09/2.14 | (24) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (difference(v2, v1) = v3) | ~ (member(v0, v3) = 0) | ? [v4] : ( ~ (v4 = 0) & member(v0, v2) = 0 & member(v0, v1) = v4)) % 6.09/2.14 | (25) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (sum(v2) = v1) | ~ (sum(v2) = v0)) % 6.09/2.14 | (26) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (singleton(v0) = v1) | ~ (member(v0, v1) = v2)) % 6.09/2.14 | (27) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (power_set(v2) = v1) | ~ (power_set(v2) = v0)) % 6.09/2.14 | (28) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (unordered_pair(v3, v2) = v1) | ~ (unordered_pair(v3, v2) = v0)) % 6.09/2.14 | (29) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (intersection(v3, v2) = v1) | ~ (intersection(v3, v2) = v0)) % 6.09/2.14 | (30) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (singleton(v2) = v1) | ~ (singleton(v2) = v0)) % 6.09/2.14 | (31) ! [v0] : ! [v1] : ! [v2] : ( ~ (power_set(v1) = v2) | ~ (member(v0, v2) = 0) | subset(v0, v1) = 0) % 6.09/2.14 | (32) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (difference(v3, v2) = v1) | ~ (difference(v3, v2) = v0)) % 6.09/2.14 | (33) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (product(v2) = v1) | ~ (product(v2) = v0)) % 6.09/2.14 | (34) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (power_set(v1) = v2) | ~ (member(v0, v2) = v3) | ? [v4] : ( ~ (v4 = 0) & subset(v0, v1) = v4)) % 6.09/2.14 | (35) intersection(all_0_4_4, all_0_5_5) = all_0_3_3 % 6.09/2.14 | (36) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (singleton(v1) = v2) | ~ (member(v0, v2) = 0)) % 6.09/2.14 | (37) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (intersection(v1, v2) = v3) | ~ (member(v0, v3) = 0) | (member(v0, v2) = 0 & member(v0, v1) = 0)) % 6.09/2.14 | (38) equal_set(all_0_3_3, all_0_1_1) = all_0_0_0 % 6.09/2.14 | (39) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (subset(v0, v1) = v2) | ? [v3] : ? [v4] : ( ~ (v4 = 0) & member(v3, v1) = v4 & member(v3, v0) = 0)) % 6.09/2.15 | (40) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | ~ (difference(v2, v1) = v3) | ~ (member(v0, v3) = v4) | ? [v5] : ? [v6] : (member(v0, v2) = v5 & member(v0, v1) = v6 & ( ~ (v5 = 0) | v6 = 0))) % 6.09/2.15 | % 6.09/2.15 | Instantiating formula (22) with all_0_0_0, all_0_1_1, all_0_3_3 and discharging atoms equal_set(all_0_3_3, all_0_1_1) = all_0_0_0, yields: % 6.09/2.15 | (41) all_0_0_0 = 0 | ? [v0] : ? [v1] : (subset(all_0_1_1, all_0_3_3) = v1 & subset(all_0_3_3, all_0_1_1) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0))) % 6.09/2.15 | % 6.09/2.15 +-Applying beta-rule and splitting (41), into two cases. % 6.09/2.15 |-Branch one: % 6.09/2.15 | (42) all_0_0_0 = 0 % 6.09/2.15 | % 6.09/2.15 | Equations (42) can reduce 12 to: % 6.09/2.15 | (43) $false % 6.09/2.15 | % 6.09/2.15 |-The branch is then unsatisfiable % 6.09/2.15 |-Branch two: % 6.09/2.15 | (12) ~ (all_0_0_0 = 0) % 6.09/2.15 | (45) ? [v0] : ? [v1] : (subset(all_0_1_1, all_0_3_3) = v1 & subset(all_0_3_3, all_0_1_1) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0))) % 6.09/2.15 | % 6.09/2.15 | Instantiating (45) with all_14_0_8, all_14_1_9 yields: % 6.09/2.15 | (46) subset(all_0_1_1, all_0_3_3) = all_14_0_8 & subset(all_0_3_3, all_0_1_1) = all_14_1_9 & ( ~ (all_14_0_8 = 0) | ~ (all_14_1_9 = 0)) % 6.09/2.15 | % 6.09/2.15 | Applying alpha-rule on (46) yields: % 6.09/2.15 | (47) subset(all_0_1_1, all_0_3_3) = all_14_0_8 % 6.09/2.15 | (48) subset(all_0_3_3, all_0_1_1) = all_14_1_9 % 6.09/2.15 | (49) ~ (all_14_0_8 = 0) | ~ (all_14_1_9 = 0) % 6.09/2.15 | % 6.09/2.15 | Instantiating formula (39) with all_14_0_8, all_0_3_3, all_0_1_1 and discharging atoms subset(all_0_1_1, all_0_3_3) = all_14_0_8, yields: % 6.09/2.15 | (50) all_14_0_8 = 0 | ? [v0] : ? [v1] : ( ~ (v1 = 0) & member(v0, all_0_1_1) = 0 & member(v0, all_0_3_3) = v1) % 6.09/2.15 | % 6.09/2.15 | Instantiating formula (39) with all_14_1_9, all_0_1_1, all_0_3_3 and discharging atoms subset(all_0_3_3, all_0_1_1) = all_14_1_9, yields: % 6.09/2.15 | (51) all_14_1_9 = 0 | ? [v0] : ? [v1] : ( ~ (v1 = 0) & member(v0, all_0_1_1) = v1 & member(v0, all_0_3_3) = 0) % 6.09/2.15 | % 6.09/2.15 +-Applying beta-rule and splitting (49), into two cases. % 6.09/2.15 |-Branch one: % 6.09/2.15 | (52) ~ (all_14_0_8 = 0) % 6.09/2.15 | % 6.09/2.15 +-Applying beta-rule and splitting (50), into two cases. % 6.09/2.15 |-Branch one: % 6.09/2.15 | (53) all_14_0_8 = 0 % 6.09/2.15 | % 6.09/2.15 | Equations (53) can reduce 52 to: % 6.09/2.15 | (43) $false % 6.09/2.15 | % 6.09/2.15 |-The branch is then unsatisfiable % 6.09/2.15 |-Branch two: % 6.09/2.15 | (52) ~ (all_14_0_8 = 0) % 6.09/2.15 | (56) ? [v0] : ? [v1] : ( ~ (v1 = 0) & member(v0, all_0_1_1) = 0 & member(v0, all_0_3_3) = v1) % 6.09/2.15 | % 6.09/2.15 | Instantiating (56) with all_42_0_10, all_42_1_11 yields: % 6.09/2.15 | (57) ~ (all_42_0_10 = 0) & member(all_42_1_11, all_0_1_1) = 0 & member(all_42_1_11, all_0_3_3) = all_42_0_10 % 6.09/2.15 | % 6.09/2.15 | Applying alpha-rule on (57) yields: % 6.09/2.15 | (58) ~ (all_42_0_10 = 0) % 6.09/2.15 | (59) member(all_42_1_11, all_0_1_1) = 0 % 6.09/2.15 | (60) member(all_42_1_11, all_0_3_3) = all_42_0_10 % 6.09/2.15 | % 6.09/2.15 | Instantiating formula (37) with all_0_2_2, all_0_5_5, all_0_6_6, all_42_1_11 and discharging atoms intersection(all_0_6_6, all_0_5_5) = all_0_2_2, yields: % 6.09/2.15 | (61) ~ (member(all_42_1_11, all_0_2_2) = 0) | (member(all_42_1_11, all_0_5_5) = 0 & member(all_42_1_11, all_0_6_6) = 0) % 6.09/2.15 | % 6.09/2.15 | Instantiating formula (37) with all_0_1_1, all_0_2_2, all_0_7_7, all_42_1_11 and discharging atoms intersection(all_0_7_7, all_0_2_2) = all_0_1_1, member(all_42_1_11, all_0_1_1) = 0, yields: % 6.09/2.15 | (62) member(all_42_1_11, all_0_2_2) = 0 & member(all_42_1_11, all_0_7_7) = 0 % 6.09/2.15 | % 6.09/2.15 | Applying alpha-rule on (62) yields: % 6.09/2.15 | (63) member(all_42_1_11, all_0_2_2) = 0 % 6.09/2.15 | (64) member(all_42_1_11, all_0_7_7) = 0 % 6.09/2.15 | % 6.09/2.15 | Instantiating formula (13) with all_42_0_10, all_0_3_3, all_0_5_5, all_0_4_4, all_42_1_11 and discharging atoms intersection(all_0_4_4, all_0_5_5) = all_0_3_3, member(all_42_1_11, all_0_3_3) = all_42_0_10, yields: % 6.09/2.15 | (65) all_42_0_10 = 0 | ? [v0] : ? [v1] : (member(all_42_1_11, all_0_4_4) = v0 & member(all_42_1_11, all_0_5_5) = v1 & ( ~ (v1 = 0) | ~ (v0 = 0))) % 6.09/2.16 | % 6.09/2.16 +-Applying beta-rule and splitting (61), into two cases. % 6.09/2.16 |-Branch one: % 6.09/2.16 | (66) ~ (member(all_42_1_11, all_0_2_2) = 0) % 6.09/2.16 | % 6.09/2.16 | Using (63) and (66) yields: % 6.09/2.16 | (67) $false % 6.09/2.16 | % 6.09/2.16 |-The branch is then unsatisfiable % 6.09/2.16 |-Branch two: % 6.09/2.16 | (63) member(all_42_1_11, all_0_2_2) = 0 % 6.09/2.16 | (69) member(all_42_1_11, all_0_5_5) = 0 & member(all_42_1_11, all_0_6_6) = 0 % 6.09/2.16 | % 6.09/2.16 | Applying alpha-rule on (69) yields: % 6.09/2.16 | (70) member(all_42_1_11, all_0_5_5) = 0 % 6.09/2.16 | (71) member(all_42_1_11, all_0_6_6) = 0 % 6.09/2.16 | % 6.09/2.16 +-Applying beta-rule and splitting (65), into two cases. % 6.09/2.16 |-Branch one: % 6.09/2.16 | (72) all_42_0_10 = 0 % 6.09/2.16 | % 6.09/2.16 | Equations (72) can reduce 58 to: % 6.09/2.16 | (43) $false % 6.09/2.16 | % 6.09/2.16 |-The branch is then unsatisfiable % 6.09/2.16 |-Branch two: % 6.09/2.16 | (58) ~ (all_42_0_10 = 0) % 6.09/2.16 | (75) ? [v0] : ? [v1] : (member(all_42_1_11, all_0_4_4) = v0 & member(all_42_1_11, all_0_5_5) = v1 & ( ~ (v1 = 0) | ~ (v0 = 0))) % 6.09/2.16 | % 6.09/2.16 | Instantiating (75) with all_65_0_12, all_65_1_13 yields: % 6.09/2.16 | (76) member(all_42_1_11, all_0_4_4) = all_65_1_13 & member(all_42_1_11, all_0_5_5) = all_65_0_12 & ( ~ (all_65_0_12 = 0) | ~ (all_65_1_13 = 0)) % 6.09/2.16 | % 6.09/2.16 | Applying alpha-rule on (76) yields: % 6.09/2.16 | (77) member(all_42_1_11, all_0_4_4) = all_65_1_13 % 6.09/2.16 | (78) member(all_42_1_11, all_0_5_5) = all_65_0_12 % 6.09/2.16 | (79) ~ (all_65_0_12 = 0) | ~ (all_65_1_13 = 0) % 6.09/2.16 | % 6.09/2.16 | Instantiating formula (3) with all_42_1_11, all_0_5_5, all_65_0_12, 0 and discharging atoms member(all_42_1_11, all_0_5_5) = all_65_0_12, member(all_42_1_11, all_0_5_5) = 0, yields: % 6.09/2.16 | (80) all_65_0_12 = 0 % 6.09/2.16 | % 6.09/2.16 +-Applying beta-rule and splitting (79), into two cases. % 6.09/2.16 |-Branch one: % 6.09/2.16 | (81) ~ (all_65_0_12 = 0) % 6.09/2.16 | % 6.09/2.16 | Equations (80) can reduce 81 to: % 6.09/2.16 | (43) $false % 6.09/2.16 | % 6.09/2.16 |-The branch is then unsatisfiable % 6.09/2.16 |-Branch two: % 6.09/2.16 | (80) all_65_0_12 = 0 % 6.09/2.16 | (84) ~ (all_65_1_13 = 0) % 6.09/2.16 | % 6.09/2.16 | Instantiating formula (13) with all_65_1_13, all_0_4_4, all_0_6_6, all_0_7_7, all_42_1_11 and discharging atoms intersection(all_0_7_7, all_0_6_6) = all_0_4_4, member(all_42_1_11, all_0_4_4) = all_65_1_13, yields: % 6.09/2.16 | (85) all_65_1_13 = 0 | ? [v0] : ? [v1] : (member(all_42_1_11, all_0_6_6) = v1 & member(all_42_1_11, all_0_7_7) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0))) % 6.09/2.16 | % 6.30/2.16 +-Applying beta-rule and splitting (85), into two cases. % 6.30/2.16 |-Branch one: % 6.30/2.16 | (86) all_65_1_13 = 0 % 6.30/2.16 | % 6.30/2.16 | Equations (86) can reduce 84 to: % 6.30/2.16 | (43) $false % 6.30/2.16 | % 6.30/2.16 |-The branch is then unsatisfiable % 6.30/2.16 |-Branch two: % 6.30/2.16 | (84) ~ (all_65_1_13 = 0) % 6.30/2.16 | (89) ? [v0] : ? [v1] : (member(all_42_1_11, all_0_6_6) = v1 & member(all_42_1_11, all_0_7_7) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0))) % 6.30/2.16 | % 6.30/2.16 | Instantiating (89) with all_106_0_14, all_106_1_15 yields: % 6.30/2.16 | (90) member(all_42_1_11, all_0_6_6) = all_106_0_14 & member(all_42_1_11, all_0_7_7) = all_106_1_15 & ( ~ (all_106_0_14 = 0) | ~ (all_106_1_15 = 0)) % 6.30/2.16 | % 6.30/2.16 | Applying alpha-rule on (90) yields: % 6.30/2.16 | (91) member(all_42_1_11, all_0_6_6) = all_106_0_14 % 6.30/2.16 | (92) member(all_42_1_11, all_0_7_7) = all_106_1_15 % 6.30/2.16 | (93) ~ (all_106_0_14 = 0) | ~ (all_106_1_15 = 0) % 6.30/2.16 | % 6.30/2.16 | Instantiating formula (3) with all_42_1_11, all_0_6_6, all_106_0_14, 0 and discharging atoms member(all_42_1_11, all_0_6_6) = all_106_0_14, member(all_42_1_11, all_0_6_6) = 0, yields: % 6.30/2.16 | (94) all_106_0_14 = 0 % 6.30/2.16 | % 6.30/2.16 | Instantiating formula (3) with all_42_1_11, all_0_7_7, all_106_1_15, 0 and discharging atoms member(all_42_1_11, all_0_7_7) = all_106_1_15, member(all_42_1_11, all_0_7_7) = 0, yields: % 6.30/2.16 | (95) all_106_1_15 = 0 % 6.30/2.16 | % 6.30/2.16 +-Applying beta-rule and splitting (93), into two cases. % 6.30/2.16 |-Branch one: % 6.30/2.16 | (96) ~ (all_106_0_14 = 0) % 6.30/2.16 | % 6.30/2.16 | Equations (94) can reduce 96 to: % 6.30/2.16 | (43) $false % 6.30/2.16 | % 6.30/2.16 |-The branch is then unsatisfiable % 6.30/2.16 |-Branch two: % 6.30/2.16 | (94) all_106_0_14 = 0 % 6.30/2.16 | (99) ~ (all_106_1_15 = 0) % 6.30/2.16 | % 6.30/2.16 | Equations (95) can reduce 99 to: % 6.30/2.16 | (43) $false % 6.30/2.16 | % 6.30/2.16 |-The branch is then unsatisfiable % 6.30/2.17 |-Branch two: % 6.30/2.17 | (53) all_14_0_8 = 0 % 6.30/2.17 | (102) ~ (all_14_1_9 = 0) % 6.30/2.17 | % 6.30/2.17 +-Applying beta-rule and splitting (51), into two cases. % 6.30/2.17 |-Branch one: % 6.30/2.17 | (103) all_14_1_9 = 0 % 6.30/2.17 | % 6.30/2.17 | Equations (103) can reduce 102 to: % 6.30/2.17 | (43) $false % 6.30/2.17 | % 6.30/2.17 |-The branch is then unsatisfiable % 6.30/2.17 |-Branch two: % 6.30/2.17 | (102) ~ (all_14_1_9 = 0) % 6.30/2.17 | (106) ? [v0] : ? [v1] : ( ~ (v1 = 0) & member(v0, all_0_1_1) = v1 & member(v0, all_0_3_3) = 0) % 6.30/2.17 | % 6.30/2.17 | Instantiating (106) with all_42_0_16, all_42_1_17 yields: % 6.30/2.17 | (107) ~ (all_42_0_16 = 0) & member(all_42_1_17, all_0_1_1) = all_42_0_16 & member(all_42_1_17, all_0_3_3) = 0 % 6.30/2.17 | % 6.30/2.17 | Applying alpha-rule on (107) yields: % 6.30/2.17 | (108) ~ (all_42_0_16 = 0) % 6.30/2.17 | (109) member(all_42_1_17, all_0_1_1) = all_42_0_16 % 6.30/2.17 | (110) member(all_42_1_17, all_0_3_3) = 0 % 6.30/2.17 | % 6.30/2.17 | Instantiating formula (13) with all_42_0_16, all_0_1_1, all_0_2_2, all_0_7_7, all_42_1_17 and discharging atoms intersection(all_0_7_7, all_0_2_2) = all_0_1_1, member(all_42_1_17, all_0_1_1) = all_42_0_16, yields: % 6.30/2.17 | (111) all_42_0_16 = 0 | ? [v0] : ? [v1] : (member(all_42_1_17, all_0_2_2) = v1 & member(all_42_1_17, all_0_7_7) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0))) % 6.30/2.17 | % 6.30/2.17 | Instantiating formula (37) with all_0_3_3, all_0_5_5, all_0_4_4, all_42_1_17 and discharging atoms intersection(all_0_4_4, all_0_5_5) = all_0_3_3, member(all_42_1_17, all_0_3_3) = 0, yields: % 6.30/2.17 | (112) member(all_42_1_17, all_0_4_4) = 0 & member(all_42_1_17, all_0_5_5) = 0 % 6.30/2.17 | % 6.30/2.17 | Applying alpha-rule on (112) yields: % 6.30/2.17 | (113) member(all_42_1_17, all_0_4_4) = 0 % 6.30/2.17 | (114) member(all_42_1_17, all_0_5_5) = 0 % 6.30/2.17 | % 6.30/2.17 | Instantiating formula (37) with all_0_4_4, all_0_6_6, all_0_7_7, all_42_1_17 and discharging atoms intersection(all_0_7_7, all_0_6_6) = all_0_4_4, yields: % 6.30/2.17 | (115) ~ (member(all_42_1_17, all_0_4_4) = 0) | (member(all_42_1_17, all_0_6_6) = 0 & member(all_42_1_17, all_0_7_7) = 0) % 6.30/2.17 | % 6.30/2.17 +-Applying beta-rule and splitting (115), into two cases. % 6.30/2.17 |-Branch one: % 6.30/2.17 | (116) ~ (member(all_42_1_17, all_0_4_4) = 0) % 6.30/2.17 | % 6.30/2.17 | Using (113) and (116) yields: % 6.30/2.17 | (67) $false % 6.30/2.17 | % 6.30/2.17 |-The branch is then unsatisfiable % 6.30/2.17 |-Branch two: % 6.30/2.17 | (113) member(all_42_1_17, all_0_4_4) = 0 % 6.30/2.17 | (119) member(all_42_1_17, all_0_6_6) = 0 & member(all_42_1_17, all_0_7_7) = 0 % 6.30/2.17 | % 6.30/2.17 | Applying alpha-rule on (119) yields: % 6.30/2.17 | (120) member(all_42_1_17, all_0_6_6) = 0 % 6.30/2.17 | (121) member(all_42_1_17, all_0_7_7) = 0 % 6.30/2.17 | % 6.30/2.17 +-Applying beta-rule and splitting (111), into two cases. % 6.30/2.17 |-Branch one: % 6.30/2.17 | (122) all_42_0_16 = 0 % 6.30/2.17 | % 6.30/2.17 | Equations (122) can reduce 108 to: % 6.30/2.17 | (43) $false % 6.30/2.17 | % 6.30/2.17 |-The branch is then unsatisfiable % 6.30/2.17 |-Branch two: % 6.30/2.17 | (108) ~ (all_42_0_16 = 0) % 6.30/2.17 | (125) ? [v0] : ? [v1] : (member(all_42_1_17, all_0_2_2) = v1 & member(all_42_1_17, all_0_7_7) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0))) % 6.30/2.17 | % 6.30/2.17 | Instantiating (125) with all_69_0_18, all_69_1_19 yields: % 6.30/2.17 | (126) member(all_42_1_17, all_0_2_2) = all_69_0_18 & member(all_42_1_17, all_0_7_7) = all_69_1_19 & ( ~ (all_69_0_18 = 0) | ~ (all_69_1_19 = 0)) % 6.30/2.17 | % 6.30/2.17 | Applying alpha-rule on (126) yields: % 6.30/2.17 | (127) member(all_42_1_17, all_0_2_2) = all_69_0_18 % 6.30/2.17 | (128) member(all_42_1_17, all_0_7_7) = all_69_1_19 % 6.30/2.17 | (129) ~ (all_69_0_18 = 0) | ~ (all_69_1_19 = 0) % 6.30/2.17 | % 6.30/2.17 | Instantiating formula (3) with all_42_1_17, all_0_7_7, all_69_1_19, 0 and discharging atoms member(all_42_1_17, all_0_7_7) = all_69_1_19, member(all_42_1_17, all_0_7_7) = 0, yields: % 6.30/2.17 | (130) all_69_1_19 = 0 % 6.30/2.17 | % 6.30/2.17 +-Applying beta-rule and splitting (129), into two cases. % 6.30/2.17 |-Branch one: % 6.30/2.17 | (131) ~ (all_69_0_18 = 0) % 6.30/2.17 | % 6.30/2.17 | Instantiating formula (13) with all_69_0_18, all_0_2_2, all_0_5_5, all_0_6_6, all_42_1_17 and discharging atoms intersection(all_0_6_6, all_0_5_5) = all_0_2_2, member(all_42_1_17, all_0_2_2) = all_69_0_18, yields: % 6.30/2.17 | (132) all_69_0_18 = 0 | ? [v0] : ? [v1] : (member(all_42_1_17, all_0_5_5) = v1 & member(all_42_1_17, all_0_6_6) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0))) % 6.30/2.17 | % 6.30/2.17 +-Applying beta-rule and splitting (132), into two cases. % 6.30/2.17 |-Branch one: % 6.30/2.17 | (133) all_69_0_18 = 0 % 6.30/2.18 | % 6.30/2.18 | Equations (133) can reduce 131 to: % 6.30/2.18 | (43) $false % 6.30/2.18 | % 6.30/2.18 |-The branch is then unsatisfiable % 6.30/2.18 |-Branch two: % 6.30/2.18 | (131) ~ (all_69_0_18 = 0) % 6.30/2.18 | (136) ? [v0] : ? [v1] : (member(all_42_1_17, all_0_5_5) = v1 & member(all_42_1_17, all_0_6_6) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0))) % 6.30/2.18 | % 6.30/2.18 | Instantiating (136) with all_110_0_22, all_110_1_23 yields: % 6.30/2.18 | (137) member(all_42_1_17, all_0_5_5) = all_110_0_22 & member(all_42_1_17, all_0_6_6) = all_110_1_23 & ( ~ (all_110_0_22 = 0) | ~ (all_110_1_23 = 0)) % 6.30/2.18 | % 6.30/2.18 | Applying alpha-rule on (137) yields: % 6.30/2.18 | (138) member(all_42_1_17, all_0_5_5) = all_110_0_22 % 6.30/2.18 | (139) member(all_42_1_17, all_0_6_6) = all_110_1_23 % 6.30/2.18 | (140) ~ (all_110_0_22 = 0) | ~ (all_110_1_23 = 0) % 6.30/2.18 | % 6.30/2.18 | Instantiating formula (3) with all_42_1_17, all_0_5_5, all_110_0_22, 0 and discharging atoms member(all_42_1_17, all_0_5_5) = all_110_0_22, member(all_42_1_17, all_0_5_5) = 0, yields: % 6.30/2.18 | (141) all_110_0_22 = 0 % 6.30/2.18 | % 6.30/2.18 | Instantiating formula (3) with all_42_1_17, all_0_6_6, all_110_1_23, 0 and discharging atoms member(all_42_1_17, all_0_6_6) = all_110_1_23, member(all_42_1_17, all_0_6_6) = 0, yields: % 6.30/2.18 | (142) all_110_1_23 = 0 % 6.30/2.18 | % 6.30/2.18 +-Applying beta-rule and splitting (140), into two cases. % 6.30/2.18 |-Branch one: % 6.30/2.18 | (143) ~ (all_110_0_22 = 0) % 6.30/2.18 | % 6.30/2.18 | Equations (141) can reduce 143 to: % 6.30/2.18 | (43) $false % 6.30/2.18 | % 6.30/2.18 |-The branch is then unsatisfiable % 6.30/2.18 |-Branch two: % 6.30/2.18 | (141) all_110_0_22 = 0 % 6.30/2.18 | (146) ~ (all_110_1_23 = 0) % 6.30/2.18 | % 6.30/2.18 | Equations (142) can reduce 146 to: % 6.30/2.18 | (43) $false % 6.30/2.18 | % 6.30/2.18 |-The branch is then unsatisfiable % 6.30/2.18 |-Branch two: % 6.30/2.18 | (133) all_69_0_18 = 0 % 6.30/2.18 | (149) ~ (all_69_1_19 = 0) % 6.30/2.18 | % 6.30/2.18 | Equations (130) can reduce 149 to: % 6.30/2.18 | (43) $false % 6.30/2.18 | % 6.30/2.18 |-The branch is then unsatisfiable % 6.30/2.18 % SZS output end Proof for theBenchmark % 6.30/2.18 % 6.30/2.18 1505ms %------------------------------------------------------------------------------